In a series circuit containing a resistor and inductor, what is the phase relationship between current and voltage?

In a series circuit containing a resistor and inductor, what is the phase relationship between current and voltage?

• A. The current lags the voltage by φ = arctan(ωL / R)
• B. The current leads the voltage by φ = arctan(ωL / R)
• C. The current is in phase with the voltage
• D. The current leads the voltage by φ = arctan(R / ωL)

Answer: (A)

In a series RL circuit, the inductor adds inductive reactance, so the total impedance has a real part R and an imaginary part ωL. The impedance angle is φ = arctan(ωL / R). Since the current is V divided by this impedance, the current carries the opposite phase to the voltage, meaning the current lags the voltage by φ. As frequency rises, φ grows toward 90 degrees, reflecting a stronger lag from the inductive effect. The idea that the current leads the voltage would only apply to a capacitive element, and the current being in phase would be true for a pure resistor. The form with arctan(R / ωL) would not match the actual impedance angle for an inductor.

In a series RL circuit, the inductor adds inductive reactance, so the total impedance has a real part R and an imaginary part ωL. The impedance angle is φ = arctan(ωL / R). Since the current is V divided by this impedance, the current carries the opposite phase to the voltage, meaning the current lags the voltage by φ. As frequency rises, φ grows toward 90 degrees, reflecting a stronger lag from the inductive effect. The idea that the current leads the voltage would only apply to a capacitive element, and the current being in phase would be true for a pure resistor. The form with arctan(R / ωL) would not match the actual impedance angle for an inductor.